Preheat your grill to medium-high heat.
In a small bowl, mix together olive oil, garlic powder, onion powder, cumin, smoked paprika, salt, and pepper. Rub this mixture all over the chicken breasts.
Place the chicken on the grill and cook for about 6-7 minutes on each side, or until the internal temperature reaches 165°F.
During the last few minutes of grilling, spoon salsa verde over each chicken breast and top with shredded pepper jack cheese. Close the grill lid and allow the cheese to melt, about 2-3 minutes.
Remove the chicken from the grill and let it rest for 5 minutes. Garnish with fresh cilantro before serving.